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"Springes" (not springs) are traps. Hamlet is all about people trying to trap other people. First we have Claudius and Polonius trying to trap Hamlet into making some admission about the cause of his apparent lunacy. The bait they use in these traps is Rosencrantz and Guildenstern, then Ophelia, and finally Gertrude. Meanwhile Hamlet sets a trap "The Mousetrap" to get a confession of guilt out of Claudius and it works. By the end of act three, Hamlet and Claudius no longer need to set traps for information. Claudius sends Hamlet to England to collect Danegeld, but it is really a trap to kill Hamlet. Hamlet is not caught, but Rosencrantz and Guildenstern are "hoist with their own petard" and die. Claudius and Laertes set new traps for Hamlet, but these end up killing Laertes and Gertrude and exposing Claudius, enabling Hamlet to kill him without opposition from whoever is left alive at that point.
does* and it's a duel that was set up before by Laertes and Claudius to kill Hamlet. For Laertes because Claudius told him that Hamelt murdered his brother and for Claudius so Hamlet doesn't spill the secret that Claudius murdered Senior Hamlet.
Hamlet doesn't actually stage a play called The Mousetrap. He asks the travelling players (The Tragedians of the City) to put on The Murder of Gonzago, which is the real name of the play. Hamlet calls it the Mousetrap because his purpose in asking them to play it is to trap Claudius into a confession of guilt.
Hamlet learns from the Ghost of his father that his father was killed by his uncle, who has since married Hamlet's mother. Hamlet decides to act crazy while figuring out what to do. His uncle Claudius sets spies on him because of his crazy behaviour. Hamlet confirms that the Ghost was telling the truth by putting on a play mirroring the murder of his father. Unfortunately this also tips Claudius off (he was pretty suspicious anyway) Hamlet catches and kills a spy in his mother's bedroom. Unfortunately it is the king's advisor Polonius. Claudius sends Hamlet to England. Polonius's son Laertes comes from France to revenge his father. Claudius tells him that Hamlet had killed Polonius. Hamlet doesn't get to England because of pirates, and returns to Denmark. Claudius and Laertes set up a Fencing match where Hamlet is to be murdered by an unbuttoned poisoned sword and a poisoned cup of wine. Hamlet gets cut by the poisoned sword but so does Laertes, and Hamlet's mother drinks the poisoned wine. Before he dies, Hamlet stabs and poisons Claudius to death.
Hamlet's plan is to kill his uncle whose name is Claudius. He wants to kill him because he saw his fathers ghost who told him that his brother poisoned him therefore Hamlet's father wants Hamlet to avenge him by killing his brother Claudius.
In the final scene, Laertes and Claudius have set in motion plans to have Hamlet killed. The question is, Will they succeed? and Will Hamlet ever get around to killing Claudius? The moment Hamlet is touched by Laertes's sword, we know the answer to the first question is "yes". There are still a few moments of suspense before we find out the answer to the second.
They are virtually indistinguishable, as if they were clones or identical twins. Claudius mixes them up and Gertrude has to set him straight
Claudius and Gertrude set Rosencrantz and Guildenstern to spy on Hamlet to discover the cause of his apparent madness
Basically, he knows that Hamlet usually walks alone through the lobby of the castle, and, at such a time, they (Polonius and Claudius) could hide behind an arras (a curtain or wall hanging) while Ophelia confronts Hamlet, allowing them to see for themselves whether Hamlet's madness really emanates from his love for her.
There would have been a trap door.
Polonius dies. Ophelia dies. Claudius dies. Hamlet dies. Hamlet returns home for his father's funeral. Hamlet stages a play to prove Claudius's guilt. Ophelia drowns in a river. Hamlet and Laertes duel. Hamlet returns to Denmark to bury his father. Hamlet kills Polonius. Ophelia is found dead. Laertes and Hamlet duel.
The mouse trap is the play inside the play. Hamlet crates a play simulating his father's death in front of his uncle. Hamlet expects his uncle to react in order to show that he's the murderer.